Question

In an AP the 9tgh term is 73 and the 4th term is 43. what is the sum of the first twenty terms

Answer 1

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Answer 2

Step-by-step explanation:

Given:

• 9th term of the AP = 73
• 4th term of the AP = 43

To find:

• Sum of twenty terms S(20)

Important formulae:

Term formula: To find nth term of an AP

$a(n) = a + (n - 1)d$

where,

• a = first term of an AP
• d = common difference

Sum formula: To find sum of n terms of an AP

$s(n) = \frac{n}{2} (2a + (n - 1)d)$

where,

• a = first term of an AP
• d = common difference

Solution:

a(9) = 73

=> a + (9 - 1)d = 73

=> a + 8d = 73 ( Eq 1)

a(4) = 43

=> a + (4 - 1)d = 43

=> a + 3d = 43 (Eq 2)

Subtracting Eq 2 from Eq 1, we get

a + 8d - ( a + 3d ) = 73 - 43

=> 5d = 30

=> d = 6

Putting d = 6 in Eq 2, we get

a + 3(6) = 43

=> a + 18 = 43

=> a = 25

Sum of 20 terms s(20):

Putting a = 25 & d = 6, we get

$s(20) = \frac{20}{2} (2(25) + (20 - 1)6)$

$s(20) = 10(50 + 19(6))$

$s(20) = 10(50 + 114)$

$s(20) = 10(164)$

$s(20) = 1640$